Chaps on rocky peak finally broadcast anguish (7)
I believe the answer is:
torment
'anguish' is the definition.
(tormenting is a kind of anguishing)
'chaps on rocky peak finally broadcast' is the wordplay.
'chaps' becomes 'men' (I've seen this before).
'on' is a charade indicator (letters next to each other).
'rocky peak' becomes 'tor' (I've seen this before).
'finally' suggests the final letters.
The final letter of 'broadcast' is 't'.
'men' put after 'tor' is 'tormen'.
'tormen'+'t'='TORMENT'
(Other definitions for torment that I've seen before include "Punish" , "Severe pain" , "Agony of mind" , "Anguish" , "Pester annoyingly" .)